fraction of cos 45 degrees

cos45 degrees = sqrt(2) / 2.

You can draw a right angled isosceles triangle.

Let the equal sides by 1 unit

The equal angles will be 45 degrees

Using Pythagoras' theorum you can determing that the hypotenuse is sqrt(2)

Then you can reas cos 45degrees straight off the triangle

$$cos 45 = \frac{1}{\sqrt2}\\$$

if you want to have a rational denominator then

$$cos 45 = \frac{1}{\sqrt2}=\frac{1}{\sqrt2}\times \frac{\sqrt2}{\sqrt2}=\frac{\sqrt2}{2}\\$$